Legere said his company is the only carrier capable of offering an unlimited-only data plan.
"It's very, very exciting, and it's a big change, and I challenge the whole rest of the industry to figure out how to do it," he said Thursday in an interview on CNBC's "Squawk on the Street."
T-Mobile US on Thursday announced it would abandon traditional data plan pricing and offer unlimited talk, text and data under a new program called T-Mobile One. In a video blog, Legere asserted AT&T and Verizon's network and technology would not allow them to follow suit.
But as T-Mobile was announcing its plan, Sprint also said it would launch an unlimited plan.
T-Mobile One would cost customers $70 for the first line, $50 for the second and $20 for each additional line on a shared plan, up to eight users. Sprint's Unlimited Freedom Plan is offering $60 for the first line and $40 for the next. Each additional line will cost $30, up to 10 lines. Both plans would charge extra to stream high-definition video.
In a string of tweets, Sprint CEO Marcelo Claure said the company had been conducting test trials and called Legere a con artist.
Legere fired back on "Squawk on the Street," citing a Bloomberg report that Sprint-owner SoftBank is still interested in buying T-Mobile US.
"Isn't that sad, actually, that he tweeted out. ... Is that the guy whose owner woke up yesterday and panted that he loves T-Mobile? I mean, the Verizon guy may have switched to Sprint, but I think the Sprint owner switched to T-Mobile," he said, referring to Sprint's recruitment of Verizon's former spokesman.
Legere insinuated that Claure was upset because he got scooped. "Just copy and paste everything I do and you'll be fine," he said.
But Claure denied his company was riding T-Mobile's coattails, saying it was Legere who copied Sprint's plan.
"What happened is something pretty simple. We started testing this a week ago. We were going to start tomorrow. What John did, unfortunately, is he basically copied our rate plans and called for an emergency press release and he's not even ready to launch until September 6," Claure told "Squawk on the Street" in a phone interview following Legere's appearance on CNBC.
"Sorry, to me, that's a con artist," he said.
Claure was named CEO at Sprint after the company dropped a bid to purchase T-Mobile in 2014 in the face of opposition from regulators. Claure said he still believes a combination of Sprint and T-Mobile would create a more formidable rival to AT&T and Verizon, but said Legere might not survive a merger.
"I don't think it's sad. I mean, it might be sad for him because if that were to happen, he'll probably get put out," he said.
T-Mobile's announcement on Thursday was the latest in a string of moves aimed at setting the company apart from its rivals as an "Un-carrier." In June, it announced it would give customers shares of its common stock.
T-Mobile US stock is up nearly 20 percent this year, compared with a 66.5-percent increase in Sprint's stock price.